= Mangasarian–Fromovitz constraint qualification
{c}
= MFCQ
{c}
{synonym}
At a feasible point for smooth $h=0$, $g\geq0$, the equality gradients must be independent and there must be a direction $v$ with $Dh\,v=0$ and $Dg_i\,v>0$ for every active inequality. It supplies a first-order direction strictly into all active inequality constraints while respecting the equality tangent space. This <constraint qualification> ensures the usual <Karush-Kuhn-Tucker conditions> are necessary for local optimality. For a strictly convex quadratic inequality restricted to an affine equality space, it holds at every feasible point exactly when a strictly feasible point exists; moving from a boundary point toward a strictly feasible point supplies the required direction.
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